%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:57:36 EDT 2022
% Result : Unsatisfiable 1.67s 1.85s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1)),
file('GRP665-11.p',unknown),
[] ).
cnf(3,axiom,
mult(A,ld(A,B)) = B,
file('GRP665-11.p',unknown),
[] ).
cnf(6,axiom,
ld(A,mult(A,B)) = B,
file('GRP665-11.p',unknown),
[] ).
cnf(9,axiom,
rd(mult(A,B),B) = A,
file('GRP665-11.p',unknown),
[] ).
cnf(15,axiom,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('GRP665-11.p',unknown),
[] ).
cnf(16,plain,
mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,axiom,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('GRP665-11.p',unknown),
[] ).
cnf(19,axiom,
mult(op_c,A) = mult(A,op_c),
file('GRP665-11.p',unknown),
[] ).
cnf(21,plain,
mult(A,op_c) = mult(op_c,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(38,plain,
mult(rd(A,B),mult(B,C)) = mult(B,mult(ld(B,A),C)),
inference(para_into,[status(thm),theory(equality)],[16,3]),
[iquote('para_into,16.1.1.1.1,3.1.1')] ).
cnf(52,plain,
rd(mult(A,op_c),A) = op_c,
inference(para_from,[status(thm),theory(equality)],[19,9]),
[iquote('para_from,19.1.1,9.1.1.1')] ).
cnf(55,plain,
ld(op_c,mult(A,op_c)) = A,
inference(para_from,[status(thm),theory(equality)],[19,6]),
[iquote('para_from,19.1.1,5.1.1.2')] ).
cnf(71,plain,
mult(mult(A,op_c),B) = mult(op_c,mult(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,21]),55])]),
[iquote('para_into,18.1.1,21.1.1,demod,55,flip.1')] ).
cnf(78,plain,
mult(x0,mult(op_c,x1)) != mult(op_c,mult(x0,x1)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),71])]),
[iquote('back_demod,1,demod,71,flip.1')] ).
cnf(127,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,52]),6]),
[iquote('para_into,38.1.1.1,52.1.1,demod,6')] ).
cnf(150,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[127])]),
[iquote('copy,127,flip.1')] ).
cnf(151,plain,
$false,
inference(binary,[status(thm)],[150,78]),
[iquote('binary,150.1,78.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:06:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.67/1.85 ----- Otter 3.3f, August 2004 -----
% 1.67/1.85 The process was started by sandbox on n029.cluster.edu,
% 1.67/1.85 Wed Jul 27 05:06:59 2022
% 1.67/1.85 The command was "./otter". The process ID is 2974.
% 1.67/1.85
% 1.67/1.85 set(prolog_style_variables).
% 1.67/1.85 set(auto).
% 1.67/1.85 dependent: set(auto1).
% 1.67/1.85 dependent: set(process_input).
% 1.67/1.85 dependent: clear(print_kept).
% 1.67/1.85 dependent: clear(print_new_demod).
% 1.67/1.85 dependent: clear(print_back_demod).
% 1.67/1.85 dependent: clear(print_back_sub).
% 1.67/1.85 dependent: set(control_memory).
% 1.67/1.85 dependent: assign(max_mem, 12000).
% 1.67/1.85 dependent: assign(pick_given_ratio, 4).
% 1.67/1.85 dependent: assign(stats_level, 1).
% 1.67/1.85 dependent: assign(max_seconds, 10800).
% 1.67/1.85 clear(print_given).
% 1.67/1.85
% 1.67/1.85 list(usable).
% 1.67/1.85 0 [] A=A.
% 1.67/1.85 0 [] mult(A,ld(A,B))=B.
% 1.67/1.85 0 [] ld(A,mult(A,B))=B.
% 1.67/1.85 0 [] mult(rd(A,B),B)=A.
% 1.67/1.85 0 [] rd(mult(A,B),B)=A.
% 1.67/1.85 0 [] mult(A,unit)=A.
% 1.67/1.85 0 [] mult(unit,A)=A.
% 1.67/1.85 0 [] mult(A,mult(B,C))=mult(rd(mult(A,B),A),mult(A,C)).
% 1.67/1.85 0 [] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.85 0 [] mult(op_c,A)=mult(A,op_c).
% 1.67/1.85 0 [] mult(mult(x0,op_c),x1)!=mult(x0,mult(op_c,x1)).
% 1.67/1.85 end_of_list.
% 1.67/1.85
% 1.67/1.85 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.85
% 1.67/1.85 All clauses are units, and equality is present; the
% 1.67/1.85 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.85
% 1.67/1.85 dependent: set(knuth_bendix).
% 1.67/1.85 dependent: set(anl_eq).
% 1.67/1.85 dependent: set(para_from).
% 1.67/1.85 dependent: set(para_into).
% 1.67/1.85 dependent: clear(para_from_right).
% 1.67/1.85 dependent: clear(para_into_right).
% 1.67/1.85 dependent: set(para_from_vars).
% 1.67/1.85 dependent: set(eq_units_both_ways).
% 1.67/1.85 dependent: set(dynamic_demod_all).
% 1.67/1.85 dependent: set(dynamic_demod).
% 1.67/1.85 dependent: set(order_eq).
% 1.67/1.85 dependent: set(back_demod).
% 1.67/1.85 dependent: set(lrpo).
% 1.67/1.85
% 1.67/1.85 ------------> process usable:
% 1.67/1.85 ** KEPT (pick-wt=11): 1 [] mult(mult(x0,op_c),x1)!=mult(x0,mult(op_c,x1)).
% 1.67/1.85
% 1.67/1.85 ------------> process sos:
% 1.67/1.85 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.67/1.85 ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.67/1.85 ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.67/1.85 ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.67/1.85 ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.67/1.85 ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.67/1.85 ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.67/1.85 ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.67/1.85 ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.67/1.85 ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.67/1.85 ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.67/1.85 ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.67/1.85 ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.67/1.85 ** KEPT (pick-wt=15): 16 [copy,15,flip.1] mult(rd(mult(A,B),A),mult(A,C))=mult(A,mult(B,C)).
% 1.67/1.85 ---> New Demodulator: 17 [new_demod,16] mult(rd(mult(A,B),A),mult(A,C))=mult(A,mult(B,C)).
% 1.67/1.85 ** KEPT (pick-wt=15): 18 [] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.85 ** KEPT (pick-wt=7): 19 [] mult(op_c,A)=mult(A,op_c).
% 1.67/1.85 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.67/1.85 >>>> Starting back demodulation with 4.
% 1.67/1.85 >>>> Starting back demodulation with 6.
% 1.67/1.85 >>>> Starting back demodulation with 8.
% 1.67/1.85 >>>> Starting back demodulation with 10.
% 1.67/1.85 >>>> Starting back demodulation with 12.
% 1.67/1.85 >>>> Starting back demodulation with 14.
% 1.67/1.85 >>>> Starting back demodulation with 17.
% 1.67/1.85 ** KEPT (pick-wt=15): 20 [copy,18,flip.1] mult(mult(A,B),ld(B,mult(C,B)))=mult(mult(A,C),B).
% 1.67/1.85 ** KEPT (pick-wt=7): 21 [copy,19,flip.1] mult(A,op_c)=mult(op_c,A).
% 1.67/1.85 Following clause subsumed by 18 during input processing: 0 [copy,20,flip.1] mult(mult(A,B),C)=mult(mult(A,C),ld(C,mult(B,C))).
% 1.67/1.85 Following clause subsumed by 19 during input processing: 0 [copy,21,flip.1] mult(op_c,A)=mult(A,op_c).
% 1.67/1.85
% 1.67/1.85 ======= end of input processing =======
% 1.67/1.85
% 1.67/1.85 =========== start of search ===========
% 1.67/1.85
% 1.67/1.85 -------- PROOF --------
% 1.67/1.85
% 1.67/1.85 ----> UNIT CONFLICT at 0.00 sec ----> 151 [binary,150.1,78.1] $F.
% 1.67/1.85
% 1.67/1.85 Length of proof is 9. Level of proof is 4.
% 1.67/1.85
% 1.67/1.85 ---------------- PROOF ----------------
% 1.67/1.85 % SZS status Unsatisfiable
% 1.67/1.85 % SZS output start Refutation
% See solution above
% 1.67/1.85 ------------ end of proof -------------
% 1.67/1.85
% 1.67/1.85
% 1.67/1.85 Search stopped by max_proofs option.
% 1.67/1.85
% 1.67/1.85
% 1.67/1.85 Search stopped by max_proofs option.
% 1.67/1.85
% 1.67/1.85 ============ end of search ============
% 1.67/1.85
% 1.67/1.85 -------------- statistics -------------
% 1.67/1.85 clauses given 26
% 1.67/1.85 clauses generated 257
% 1.67/1.85 clauses kept 90
% 1.67/1.85 clauses forward subsumed 218
% 1.67/1.85 clauses back subsumed 0
% 1.67/1.85 Kbytes malloced 1953
% 1.67/1.85
% 1.67/1.85 ----------- times (seconds) -----------
% 1.67/1.85 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.85 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.85
% 1.67/1.85 That finishes the proof of the theorem.
% 1.67/1.85
% 1.67/1.85 Process 2974 finished Wed Jul 27 05:07:00 2022
% 1.67/1.85 Otter interrupted
% 1.67/1.85 PROOF FOUND
%------------------------------------------------------------------------------